Arsene Wenger's team have conceded only two goals so far in the Premier League - the joint-fewest in the division along with table toppers Chelsea - and are unbeaten through their opening five contests.
Bould replaced Pat Rice as Wenger's No.2 following the retirement of the 63-year-old at the end of last season and Gibbs praised the positive effect of his attention to detail and training methods.
| ARSENAL LATEST
|7/1||Arsenal are 7/1 to beat Chelsea 1-0 with bet365|
"We just looked at where we were going wrong – and attention to detail comes into it a lot with Steve Bould. He's very focused on the small things.
"He played quite recently and we do a lot more stuff by splitting the team into separate training sessions. We are getting a good understanding."
Gibbs was particularly grateful for the influence of Bould given that the former Arsenal defender recommended to Wenger that the full-back be promoted to first-team training after impressing for the club's youth sides.
"Steve was the one who said to the boss to put me in to train with the first-team for the first time," he revealed.
"Now he's working with us I want to show him my appreciation for what he's done and how he helped me. I feel I want to give that back and show him he was right in what he did for me."